Lecture 16 1 Worst-Case vs. Average-Case Complexity
... how difficult the problem is to solve for an instance chosen randomly from some distribution. It may be the case for a certain problem that hard instances exist but are extremely rare. Many reductions use very specifically constructed problems, so their conclusions may not apply to “average” problem ...
... how difficult the problem is to solve for an instance chosen randomly from some distribution. It may be the case for a certain problem that hard instances exist but are extremely rare. Many reductions use very specifically constructed problems, so their conclusions may not apply to “average” problem ...
Bayes` theorem
... that there are just 10 balls in the machine. This is because the probability that “3” comes out given that balls 1-10 are in the machine is 10%, whereas the probability that this ball comes out given that balls numbered 1-10,000 are in the machine is only 0.01%. (Note that, whichever hypothesis you ...
... that there are just 10 balls in the machine. This is because the probability that “3” comes out given that balls 1-10 are in the machine is 10%, whereas the probability that this ball comes out given that balls numbered 1-10,000 are in the machine is only 0.01%. (Note that, whichever hypothesis you ...
Chapter 3: Random Graphs 3.1 G(n,p) model ( )1 Chapter 3
... vertices. It is also very simple to study these distributions in G ( n, p ) since the degree of each vertex is the sum of n-1 independent random variables. Since we will be dealing with graphs where n, the number of vertices, is large, from here on we replace n-1 by n to simplify formulas. Consider ...
... vertices. It is also very simple to study these distributions in G ( n, p ) since the degree of each vertex is the sum of n-1 independent random variables. Since we will be dealing with graphs where n, the number of vertices, is large, from here on we replace n-1 by n to simplify formulas. Consider ...
and “Random” to Meager, Shy, etc.
... intuitively mean by properties. Indeed, in statistics, properties must be well defined and well described in an appropriate formal language. The corresponding sets are called definable. A set is definable if it can be uniquely described by a formula in an appropriate language. Since there are more than ...
... intuitively mean by properties. Indeed, in statistics, properties must be well defined and well described in an appropriate formal language. The corresponding sets are called definable. A set is definable if it can be uniquely described by a formula in an appropriate language. Since there are more than ...
A Characterization of Entropy in Terms of Information Loss
... Some examples may help to clarify this point. Consider the only possible map f : {a, b} → {c}. Suppose p is the probability measure on {a, b} such that each point has measure 1/2, while q is the unique probability measure on the set {c}. Then H(p) = ln 2, while H(q) = 0. The information loss associa ...
... Some examples may help to clarify this point. Consider the only possible map f : {a, b} → {c}. Suppose p is the probability measure on {a, b} such that each point has measure 1/2, while q is the unique probability measure on the set {c}. Then H(p) = ln 2, while H(q) = 0. The information loss associa ...
Probability
... Due to each student having different capabilities, this situation could never occur. It is impossible that this event will occur. ...
... Due to each student having different capabilities, this situation could never occur. It is impossible that this event will occur. ...
Multichotomous Dependent Variables I
... As with logit and probit, the coefficients do not indicate the marginal effect of the independent variables on the probabilities of y = 0, 1, 2, 3 etc. However, recall that with probit and logit you could infer the direction and statistical significance associated with increasing x on the probability of ...
... As with logit and probit, the coefficients do not indicate the marginal effect of the independent variables on the probabilities of y = 0, 1, 2, 3 etc. However, recall that with probit and logit you could infer the direction and statistical significance associated with increasing x on the probability of ...
Statistical Methods for Computational Biology Sayan Mukherjee
... Waiting for tail: My experiment is to continually toss a coin until a tail shows up. If I designate heads as h and tails as t in a toss then an elementary outcome of this experiment is a sequence of the form (hhhhh...ht). There are an infinite number of such sequences so I will not write Ω and we ca ...
... Waiting for tail: My experiment is to continually toss a coin until a tail shows up. If I designate heads as h and tails as t in a toss then an elementary outcome of this experiment is a sequence of the form (hhhhh...ht). There are an infinite number of such sequences so I will not write Ω and we ca ...